Question

Solve for x
120=1.5e^3x

Answer 1

\[120=1.5e^{3x}\]

Using the property of logs that \(\log a^n = n\log a\) take the log of both sides and solve for \(x\).

Answer 2

(divide both sides by 1.5 first to isolate the exponential on the right)

Answer 3

If you use the natural log, \(\ln e = 1\)...

Answer 4

So is the answer 26.67 for x

Answer 5

No, I don't think so...\(e^{80}\) is a big number!

Answer 6

x=5.5406x10^34

Answer 7

\[120 = 1.5e^{3x}\]Divide by 1.5
\[80 = e^{3x}\]Take natural log of both sides
\[\ln 80 = \ln e^{3x} = 3x \ln e = 3x \]
\[x=\frac{\ln 80}{3} \approx 4.932\]

Answer 8

ok got it

Answer 9

so the x=4.932

Answer 10

\[\ln 80 \approx 4.382\]
\[\frac{\ln 80}{3} \approx 1.461\]

Answer 11

ok I got that so then x=1.461

Answer 12

Must have fat-fingered the calculation the first time, that's why I always check my answers!

Answer 13

ok thanks lol

Answer 14

yes, x = 1.461.

\[120 = 1.5*e^{(3*1.461) }= 1.5*e^{4.383} = 1.5*80.07 \approx 120\]

(answer is actually a smidge less than 1.461, clearly)